In fact all the city provides is a referral service which seems to be intended for seniors. There's no reference to anyone else being eligible, though they also don't look like they're checking IDs or anything, nor does the program appear to be subsidized. And since the city doesn't refer to people who can't shovel, they manage to avoid using a term you find offensive.

That said: referring to the class of people who can't shovel their own walks as "disabled" is incorrect. Someone attempting to reply to a question about x and y people who can't shovel by including z people who also can't shovel is trying to be inclusive, even if they got their facts wrong doing it. Howling at them for that is just going to land you in a lot of killfiles.